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In A B C , prove that t a n A+t a n B+t...

In ` A B C` , prove that `t a n A+t a n B+t a n Cgeq3sqrt(3),w h e r eA ,B ,C` are acute angles.

Text Solution

Verified by Experts

In `Delta ABC`,
`tan-A+tan B+tan C=tan A tan B tan C`
Also,
`(tan A+ tan B +tan C)/(3) ge 3sqrt(tan A tan B tan C)`
or `tan A tan B tan C ge 3sqrt(tan A tan B tan C)`
or `tan^2 A tan^2 B tan^2 C ge 27`
or `tan A tan B tan C ge 3sqrt(3)`
or `tan A+tan B +tan C ge 3sqrt(3)` .
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